Question

Beer and BAC How well does the number of beers a person drinks predict his or her blood alcohol content (BAC)? Sixteen volunteers with an initial BAC of $0$drank a randomly assigned number of cans of beer. Thirty minutes later, a police officer measured their BAC. Least-squares regression was performed on the data. A residual plot and a histogram of the residuals are shown below. Check whether the conditions for performing inference about the regression model are met.

Short answer

Linear, independent, normal, equal variance, and random are the five requirements for regression inference.

As a result, all requirements have been met.

Step-by-step solution

Given Information

Sixteen volunteers with an initial BAC of $0$drank a randomly assigned number of cans of beer. Thirty minutes later, a police officer measured their BAC. Least-squares regression was performed on the data. A residual plot and a histogram of the residuals are shown below.

Explanation

The five requirements for regression inference are linear, independent, normal, equal variance, and random.

Linear: Satisfied since the residual plot's points are all centered around $0$.

Independent: Because the respondents were distributed at random, the subjects were satisfied.

Normal: The histogram is basically bell-shaped, so I'm satisfied.

Equal variance: Satisfied since the vertical spread of the residual plot points is almost the same everywhere.

Random: Because the subjects were allocated at random, I'm satisfied.